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研究生:蘇益德
研究生(外文):Jindrich Susen
論文名稱:滾珠導螺桿之摩擦力分析研究
論文名稱(外文):A study on the analysis of Friction Force for Ballscrew
指導教授:陳昭亮
指導教授(外文):Jau-Liang Chen
學位類別:碩士
校院名稱:國立中興大學
系所名稱:機械工程學系所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
畢業學年度:97
語文別:英文
論文頁數:105
中文關鍵詞:滾珠導螺桿摩擦彈液動潤滑MATLAB
外文關鍵詞:ball screwfrictionelastohydrodynamicMATLAB
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本研究主要目的,乃在於探討並改善目前有關滾珠導螺桿機構摩擦之模型。這些模型之建立,乃是依據先前應用於預測滾珠軸承與線性滑軌摩擦之模型(分別由Harris以及Tan所發展)。在本研究模擬中所使用之數據,是引用Kamalzadeh的博士論文”Precision Control of High Speed Ball Screw Drives”(高速滾珠導螺桿驅動之精密控制)中之數據,此篇博士論文主要是探討滾珠導螺桿之控制。同時,在該篇博士論文中所量測到之滾珠導螺桿之摩擦特性數據,則被用來作為不同滾珠導螺桿摩擦模型之模擬結果比較。
依據上述之數據,本研究使用MATLAB分別針對三種不同模型進行模擬評估。第一個模型是由Olaru所發展之滾珠導螺桿摩擦模型,經由模擬結果,發現了模擬之數據與模型結果中間有很大之差異性。
第二個模型則是依據黏彈性(viscoelastic)材料之摩擦模型所建立,此一模型成功地應用在預測微滾珠(micro ball)線性滑軌之摩擦。然而,由模擬結果,此一模型並無法應用在一般尺寸滾珠導螺桿之摩擦預測上。
第三個模型則是依據滾珠軸承摩擦模型所建立,為了提昇其效率,在原始之滾珠軸承模型上加了若干假設予以簡化。經由模擬之結果比較,此一模型模擬結果與上述博士論文之實驗數據相當吻合,因此,驗證了此一簡化模型是可以被接受的。
This study focuses on improvement of current friction models for ball screw mechanism. The models applied were based on models used for prediction of friction in ball bearings - Harris and linear guides - Tan. No experiment was done as a part of this study. The data for simulation were taken from PhD thesis “Precision Control of High Speed Ball Screw Drives” by Kamalzadeh which was aimed to Ball screw control. The ball screw friction characteristic data measured in his thesis was used in this study to compare various ball screw friction models.
Three models were evaluated with the available simulation data using MATLAB. The first was the ball screw friction model by Olaru. A significant miss match between the simulation data and the model results was found.
The second model was based on the model of friction for viscoelastic materials which was successfully used for prediction of friction in linear guides with micro balls. It was found that it is not useful for friction prediction in common size ball screws.
The third model used for simulation was based on friction in ball bearings. The original model used for ball bearings was simplified by several assumptions to increase efficiency. The results of this model were in a good agreement with the experimental data provided in the PhD thesis mentioned above and thus the simplifications proved to be acceptable.
Acknowledgement........... ...............................i
摘要.....................................................ii
Abstract................................................iii
Table of Contents .......................................iv
List of Tables..........................................vii
List of Figures .......................................viii
Chapter 1. Introduction.................................. 1
1.1 Background......................................... 1
1.2 Literature Review ................................. 1
1.2.1 Rolling Friction .............................. 2
1.2.2 Hydrodynamic Friction ......................... 3
1.2.3 Friction in Bearings........................... 5
1.2.4 Friction in Ball Screw ........................ 6
1.3 Motivation and Objective .......................... 6
1.4 Methodology and Structure of Thesis ............... 7
Chapter 2. The Ball Screw Mechanism...................... 9
2.1 Importance of the Ball Screw Mechanism ............ 9
2.2 The Fundamentals of Ball Screw ................... 11
2.2.1 Preloading in Ball Screw...................... 13
2.2.2 Mounting Methods ............................. 14
2.2.3 Ball Recirculation............................ 16
2.3 Errors in Ball Screws............................. 18
Chapter 3. Friction Theory and Friction Models ......... 21
3.1 Friction.......................................... 21
3.1.1 Sliding and Sliding Friction ................. 23
3.1.2 Rolling and rolling friction.................. 24
3.1.3 Frictional Behavior........................... 25
3.2 Fluid Film Lubrication ........................... 29
3.2.1 Conformal and Non conformal Surfaces ......... 29
3.2.2 Lubrication Regimes .......................... 29
3.2.3 Lambda (λ) Ratio ............................. 31
3.2.4 The Lubricating Film Thickness ................ 32
3.3 Olaru’s Model of Friction Moment................. 33
3.4 Viscoelastic Model of Rolling Friction ........... 40
3.4.1 The Transformation of Input data ............. 40
3.4.2 The Viscoelastic Model Theory ................ 45
3.4.2.1 Assumptions and Limitations of Viscoelastic
Model..................................... 45
3.4.2.2 The Definition of the Viscoelastic Model.. 47
3.5 The Simplified Model Based on Friction in Bearings 53
3.5.1 The Friction Equation ........................ 53
3.5.1.1 The Friction due to Asperity Contact ..... 53
3.5.1.2 The Friction due to Hydrodynamic Forces... 56
Chapter 4. Simulation of the Models .................... 62
4.1 Simulation Data .................................. 62
4.2 Model of Friction Moment by Olaru................. 65
4.2.1 The Verification of Olaru’s Model ........... 66
4.2.2 Results of Olaru’s Model .................... 71
4.3 Viscoelastic Model ............................... 72
4.3.1 The Solution of Viscoelastic Model in MATLAB . 72
4.3.2 Results of the Viscoelastic Model............. 76
4.3.3 Friction Generated by the Other Elements in the
System........................................ 79
4.3.4 Influence of Preload on Results of the
Viscoelastic Model............................ 82
4.3.5 Influence of the Constants of Viscoelastic Model
to Model Results...............................84
4.4 The Simplified Model Based on Friction in Bearings 86
4.4.1 The Solution of Simplified Friction Model in
MATLAB ....................................... 86
4.4.2 Results of the Simplified Friction Model...... 87
4.4.3 Influence of Different Preload on the Simplified
Friction Model................................ 90
4.4.4 The Influence of the Lubricant Viscosity on the
Simplified Friction Model Results ............ 91
Chapter 5. Conclusion and Future Work................... 94
5.1 Conclusion ....................................... 94
5.2 Future Work....................................... 95
References...............................................96
[1] O. Reynolds, “On Rolling-Friction”, Philosophical Transactions of the Royal Society of London, vol. 166, pp. 155-174, 1876
[2] J. J. Bikerman, “Effect of Surface Roughness on Rolling Friction”, Journal of Applied Physics, vol. 20, pp. 971-975, 1949
[3] H. Hertz, ‘‘Gesammelte Werke,’’ vol. I, Leipzig, 1895
[4] O. Reynolds, “On Rolling Friction” Philosophy Transaction Royal Society, 166, pp. 243–247, 1875
[5] H. Poritsky, “Stress and deflections of cylindrical bodies in contact with application to contact of gears and of locomotive wheel“, J. Appl. Mech., vol.72 pp. 191-201, 1950
[6] H. Heathcote, Proc. Inst. Automob. Eng., London, 15, 569, 1921
[7] K. Johnson, “Tangential tractions and micro-slip, Rolling Contact Phenomena”, Elsevier, Amsterdam, pp. 6–28. 1962
[8] H. L. Whittemore, and S. N. Petrenko, “Friction and Carrying Capacity of Ball and Roller Bearings”, Tech. Paper Bur. Stand., No. 201, 1921
[9] D. Tabor, “Comments on the Work Done in Rolling Friction”, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 212, No. 1111, pp. 478-479, 1952
[10] D.G. Blom, A.M. Bueche, “Theory of rolling friction for spheres”. J. Appl. Phys. vol. 30, 1725–1730, 1959
[11] R. Drutowski, “Energy losses of balls rolling on plates”, Friction and Wear, Elsevier, Amsterdam, pp. 16–35, 1959
[12] J.A. Greenwood and D. Tabor, “The friction of hard sliders on lubricated rubber: the importance of deformation losses”, Proc Phys Soc, vol. 71, pp. 989–1001, 1958
[13] F. Al-Bender, K. De Moerlooze, “A Model of the Transient Behavior of Tractive Rolling Contacts”, Mechanical Engineering Department, Division Production Engineering, Machine design and Automation, Katholieke Universiteit Leuven, Celestijnenlaan 300B, B-3001 Heverlee, Belgiim, Advances in Tribology, Article ID 214894, 2008
[14] B. J. Hamrock, “Fundamentals of Fluid Film Lubrication”, McGraw-Hill, New York, 1994
[15] O. Reynolds. “On the theory of lubrication and its application to Mr. Beauchamp Tower’s experiments, including an experimental determination of the viscosity of olive oil”. Phil. Trans. Royal Soc., 177:157–234, 1886
[16] B. Tower, “First Report on Friction Experiments,” Proc. Inst. Of
Mechanical Engineering, pp. 632-659, 1883
[17] W.B. Hardy, ”Boundary Lubrication-The Parafin Series”, Proc. R. Soc. London Ser. A, vol.100, pp. 25-39, 1922
[18] E. Trachman, and H. Cheng, “Thermal and non-Newtonian effects on traction in elastohydrodynamic contacts”, Proc. Inst. Mech. Eng., 2nd Symposium on Elastohydrodynamic Lubrication, Leeds, pp. 142–148 , 1972
[19] S. Bair and W. Winer, “A rheological model for elastohydrodynamic contacts based on primary laboratory data”, ASME Trans., J. Lubr. Technol., vol.101(3), pp.258–265, 1979
[20] B. J. Hamrock and D. Dowson, “Isothermal elastohydrodynamic lubrication of point contacts“, ASME J. of Lubrication Tech. vol. 99, 2, pp. 264-276, 1977
[21] T. Harris, “Ball motion in thrust-loaded, angular-contact ball bearings with coulomb friction”, ASME Trans., J. Lubr. Technol., vol. 93, pp. 32–38, 1971
[22] T. A. Harris, M. N. Kotzalas, “Advanced Concepts of Bearing Technology”, CRC Press, 2007
[23] T. Harris, “An analytical method to predict skidding in thrust-loaded angular-contact ball bearings”, ASME Trans., J. Lubr. Technol., vol. 93, pp. 17–24, 1971
[24] C. Walters, “The dynamics of ball bearings”, ASME Trans., J. Lubr. Technol., vol. 93(1), pp. 1–10, 1971
[25] H. Eimer, “Aus dem Gebiet der Walzlagertechnik“,Semesterentwurf, Technische Hochschule, Munchen, 1964
[26] H. Zhao, “Analysis of load distributions within solid and hollow roller bearings”, ASME Trans. J. Tribol., vol. 120, pp. 134–139, 1998
[27] H. Thomas and V. Hoersch, “Stresses due to the pressure of one elastic solid upon another”, Univ. Illinois Bull., 212, July 15, 1930
[28] M. Hartnett, “The analysis of contact stress in rolling element bearings”,ASME Trans. J. Lub. Technol., vol.101, pp.105–109, 1979
[29] T. Harris, Rolling element bearing dynamics, Wear, vol. 23, pp. 311–337, 1973
[30] C.W. Wei and J.F. Lin, “Kinematic analysis of the ball screw mechanism considering variable contact angles and elastic deformations”, Transactions of ASME, Journal of Mechanical Design, Vol.125, No. 4, pp. 717-733, 2003
[31] L. Houpert, P. Leenders, “A theoretical and experimental investigation into Rolling Bearing Friction”, Proc. Of Eurotrib Conference, Lyon, 1985
[32] L. Houpert, “Numerical and Analytical Calculations in Ball Bearings”, Proc. of Congres Roulements, Toulouse, vol. 5-7, pp.1-15, 1999
[33] L. Houpert, “Ball Bearing and Tapered Roller Bearing Torque: Analytical, Numerical and Experimental Results”, Proc of STLE Annual Meeting, Houston, May 19 – 23, 2002.
[34] D. Olaru, G. C. Puiu, L. C. Balan, V. Puiu “A New model to estimate fiction torque in a ball screw system” http://dpr.unitbv.ro/adept/asi/C2-14.pdf
[35] Ball Screw Catalogue, THK
http://www.thk.com/eng/products/class/ballscrew/index.html
[36] G. Holroyd, “The modeling and correction of ball-screw geometric, thermal and load errors on CNC machine“, PhD. Thesis University of Huddersfield, 2007
[37] M. Yang and J. Park, “Analysis of setting errors in precision ball screw machining and automatic adjustable center”, International Journal of Machine tools and Manufacture vol. 30, pp. 965-979, 1998
[38] Rolling Resistance, Wikipedia
http://en.wikipedia.org/wiki/Rolling_resistance
[39] F. Al-Bender and K. De Moerlooze, “A model of the transient behavior of tractive rolling contacts,” Advances in Tribology. vol. 2008, Article ID 214894, 2008
[40] H. Olsson , K. J. Astrom, C. Canudas de Wit, M. Gafvert , P. Lischinsky , “ Friction Models and Friction Compensation“ , Department of Automatic Control, Lund Institute of Technology, Lund University, Box 118, S-22100 LUND, Sweden, Laboratoire d’Automatique de Grenoble, CNRS-INPG-UJF, ENSIEG-INPG, B.P. 46, 38402 Grenoble, France, Control Department, EIS, ULA, Merida 5101, Venezuela, 1997
[41] R. Stribeck, “Die wesentlichen Eigenschaften der Gleit- und Rollenlager – The key qualities of sliding and roller bearings“, Zeitschrift des Vereines Seutscher Ingenieure, 46H38,39I:1342–48,1432–37, 1902
[42] E. Rabinowicz, “The nature of the static and kinetic coefficients of Friction”, Journal of Applied Physics, 22H11I:1373–79, 1951.
[43] V. Johannes and M. Green, “Role of the rate of application of the tangential force in determining the static friction coefficient”, Wear vol. 24(3), pp.381–385, 1973
[44] J. Courtney-Pratt and E. Eisner, “The effect of a tangential force on the contact of metallic bodies”, In Proceedings of the Royal Society, vol. A238, pp. 529–550, 1957
[45] “Stribeck Curve”
http://www.tribology-abc.com/abc/stribeck.htm
[46] A. Kamalzadeh, “ Precision Control of High Speed Ball Screw Drives“, PhD. Thesis University of Waterloo, Department ofMechanical Engineering, Waterloo, Ontario, Canada, 2008
[47] T. Poschel, T. Schwager and N. V. Brilliantov, , “Rolling Friction of a Hard Cylinder on a Viscous Plane”, Eur. Phys. J. B, vol.10, pp. 169–174. 1999
[48] X. Tan, A. Modafe, R. Ghodssi, “Measurement and Modeling of Dynamic Rolling Friction in Linear Microball Bearings”, Journal of Dynamic Systems, Measurement, and Control, vol. 128, pp. 891-898, 2006
[49] L. Houpert, , “An Engineering Approach to Hertzian Contact Elasticity--Part I,” in Proc. STLE/ASME Tribology Conf., Seattle, 2000, ASME Jour. Of Trib.,vol.123, pp 582-588, 2001
[50] R.S. Zhou, M. R. Hoeprich, “Torque of Tapered Roller Bearings”, Trans. Of ASME, Journal of Tribology, vol.113, pp.590-597, 1991
[51] http://www.hiwin.com/pdf/bs/Lubrication/Ball Screw%20Lubrication.pdf
[52] J.S. Arora, “Introduction to Optimum Design”, McGraw-Hill, New York, 1989
[53] Preload, Minebea Group
]http://www.eminebea.com/content/html/en/engineering/bearings/preload.shtml
[54]SKF On-line Calculator, Product tada
http://www.skf.com/skf/productcatalogue/jsp/viewers/productTableViewer.jsp? presentationType=3&lang=en&newlink=1&tableName=1_3_1
[55] U. Heisel, G. Koscsak, T. Stehle, “Thermography-based investigation into thermally induced positioning errors of feed drives by example of a ball screw”, Annals of CIRP, vol. 55, No. 1, pp. 423-426, 2006
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